Question: Solve for $x$ and $y$ using elimination. ${x-3y = 0}$ ${2x+5y = 22}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-2x+6y = 0}$ $2x+5y = 22$ Add the top and bottom equations together. $11y = 22$ $\dfrac{11y}{{11}} = \dfrac{22}{{11}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x-3y = 0}\thinspace$ to find $x$ ${x - 3}{(2)}{= 0}$ $x-6 = 0$ $x-6{+6} = 0{+6}$ ${x = 6}$ You can also plug ${y = 2}$ into $\thinspace {2x+5y = 22}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(2)}{= 22}$ ${x = 6}$